This simple illustration is easily recognizable in Freemasonry as an illustrated proof of the Pythagorean Theorem, better known in Masonry as the 47th problem of Euclid. (It is so named because it was number forty-seven in a collection of geometrical problems produced by the Alexandrian mathematician Euclid) This ubiquitous emblem is found on badges and jewels, lodge decorations and more, and has been associated with Masonry for hundreds of years.
(Most of us are familiar with the theorem from high school: “In any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the sides.” The theorem is the basis of Trigonometry.)
The 47th problem has been referred to as “the foundation of Freemasonry.” Why one of many possible solutions to a particular geometrical problem should become emblematic of Freemasonry probably has more to it the long standing tradition of Sacred Geometry, but the importance of the symbol is largely unknown.
One possibility might be found in Egypt- the historian Plutarch notes that the triangle is emblematic of the Egyptian trinity of Osiris, Isis, and Horus. The symbol has sometimes referred to as “the bride’s chair,” referring to its resemblance to the Mystical Throne of Isis.
Noted kabbalist Alan Bennet speculated that the three squares represented the magical squares of Saturn, Jupiter, and Mars. Masonic author Albert Pike, in his Morals and Dogma repeats Plutarch’s comments and suggests that the triangle represents matter (Isis), spirit (Osiris), and the union of the two (Horus)…and indeed, the sum of the two smaller squares equals the larger.
An illustration of the theorem overlaid on the Last Supper by Leonardo Da Vinci